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Wiskunde week 4, antw - Opgavencollege Wiskunde 1 1 Oktober...

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Opgavencollege Wiskunde 1, 1 Oktober 2010 Les 4 Uitwerkingen Opgavencollege Wiskunde 1 Les 4 Uitwerkingen Pag. 1/4 Opgave 1 Uit de definitie van een logaritme ( log c g c x x g = = ) volgt automatisch: log c g g c = en in het bijzonder log10 c c = en lne c c = . a) 48 7 7 log 7 48log 7 48 = = . b) log(3,4) 10 3,4 = . c) 2 2 1 ln( ) ln 2ln 2 e e e - = = - = - . d) ln(6) 6 e = . e) ( 29 5 3 15 5 2 2 5 5 5 15 log 5 5 log 5 log 5 . 2 = = = f) ( 2 2 2 2 2 log 10 log 10 2log 10 log 10 2 2 4 2 2 2 10 100 = = = = = . g) 5,01 lne 5,01. = h) 4 3 3 log 81 log 3 4. = = i) 5 log(0,00001) log(10 ) 5log10 5 - = = - = - . j) 1 lne lne 1. = = k) 3 1 1 log( ) ln( ) log(10 ) 3 1 3 2 10 e - = + = - + = Opgave 2 a) 2 1 1 1 5 2 23 2 18 9 3 3 2 2 3 3 3 x x x x x x - ⇔ - ≤ - b) ( 29 ( 29 ln(25) (1,1) 25 ln((1,1) ) ln(25) ln 1,1 ln(25) 33,77 ln 1,1 x x x x c) ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 1 1,05 6,8 1,05 0,34 1 0,66 1,05 0,66 ln 1,05 ln 0,66 0,05 ln 0,66 ln 1,05 ln 0,66 8,52 ln 1,05 x x x x x x - - - - - < ⇔ - < - = - - ⇔ - < d) 1,14 1,14 1 65 1,14 1 9,1 1.14 10,1 log 10,1 0,14 log10,1 17,65.
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